Transition from the constant ion mobility regime to the ion-atom charge-exchange regime for bounded collisional plasmas

Abstract

A numerical and analytical study of a planar, collisional, direct-current, plasma-wall problem is presented. The fluid model for the problem is first validated by comparing numerical solutions with experimental data for low-pressure (∼0.1Pa) electrode sheaths with wall potentials on the order of −100V. For electric potential, ion number density, and ion velocity, good agreement was found between theory and experiment from within the sheath out to the bulk plasma. The frictional drag resulting from ion-neutral collisions is described by a model incorporating both linear and quadratic velocity terms. In order to study the transition from the constant ion mobility regime (linear friction) to the ion-atom charge-exchange collision regime (quadratic friction), the theoretical model was examined numerically for a range of ion temperatures and ion-neutral collision rates. It was found that the solution profiles in the quasineutral plasma depend on the ion temperature. For low ion temperatures they are governed mainly by the ion-atom charge-exchange regime, whereas for high temperatures they are governed by the constant ion mobility regime. Quasineutral plasma models corresponding to these two limiting cases were solved analytically. In particular, an analytical plasma solution is given for the ion-atom charge exchange regime that includes the effects of ion inertia. In contrast to the quasineutral plasma, the sheath is always governed for low to moderate collision rates by the ion-atom charge-exchange regime, independent of the ion temperature. Varying the collision rate, it was shown that when the wall potential is sufficiently high, the sheath cannot be considered collisionless, even if the collision rate is quite small.